Hodge spaces of real toric varieties

被引：0
作者：
Valerie Hower
机构：
[1] University of Georgia,Department of Mathematics
来源：
Collectanea mathematica | 2008年 / 59卷
关键词：
Real toric variety; Hodge space; reflexive polytope; Smith-Thom; Primary 14M25; Secondary 55T99, 52B12;
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摘要：
We define the ℤ2 Hodge spacesHpq(Σ) of a rational fan Σ. If Σ is the normal fan of a reflexive polytope Δ then we use polyhedral duality to compute the Σ2 Hodge Spaces of Σ. In particular, if the cones of dimension at most e in the face fan Σ* of Δ are smooth then we computeHpq(Σ) forp <e − 1. If Σ* is a smooth fan then we completely determine the spacesHpq(Σ) and we showXΣ is maximal, meaning that the sum of the ℤ2 Betti numbers ofXΣ(ℝ) is equal to the sum of the ℤ2 Betti numbers ofXΣ(ℂ).
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页码：215 / 237
页数：22
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